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Suppose the curve goes through the point (1,3), then determine the equation of the curve

Question

Suppose the curve goes through the point (1,3), then determine the equation of the curve

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Solution

To determine the equation of a curve that goes through a specific point, such as (1, 3), we need additional information about the nature of the curve. For example, is it a linear curve, a quadratic curve, an exponential curve, etc.? Without this information, we can only provide a general approach.

Let's assume the curve is a simple linear equation of the form y=mx+b y = mx + b . Here are the steps to determine the equation:

  1. Identify the given point: The curve passes through the point (1, 3). This means when x=1 x = 1 , y=3 y = 3 .

  2. Substitute the point into the equation: Substitute x=1 x = 1 and y=3 y = 3 into the linear equation y=mx+b y = mx + b .

    3=m(1)+b 3 = m(1) + b

    Simplifying, we get:

    3=m+b 3 = m + b

  3. Determine the slope (m): To find

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